第一章之目標是透過電泳理論模型以及電泳測量提出了一種方便且快速的程序來估計金屬氧化物顆粒的表面離解/締合反應的平衡常數。在模型當中考慮了更符合實際粒子在溶液當中運動的相關因素。平衡常數通常是透過較繁瑣的電位酸鹼滴定法做實驗上的估算，且在其所使用的理論架構中，需要假設多個條件，因此所獲得的結果可能較不可靠，尤其是當離解反應的平衡常數與締合反應的平衡常數之間的差異較小時。此外，本篇另一貢獻是當未知粒子表面解離/締合官能基密度時，也能夠估計其平衡常數，因此它比以往的方法更加方便和準確。由本方法應用於分散在NaCl水溶液中的SiO2和TiO2奈米粒子的情況，做為檢驗本方法的適用性。
第二章是探討可改質的子彈形奈米孔道之電動力學現象。本篇重點是透過數值模擬方式驗證了其改質層的立體障礙效應。在模型當中，奈米孔道壁面上包含來自原薄膜基材的表面官能基之表面電荷，及在改質層的厚度中的空間電荷。由數值模擬結果得知改質層的空間效應將影響奈米孔的離子傳輸行為，且因施加偏壓會造成電滲流（EOF），會通過該層影響離子分佈，其影響程度取決於該層的柔軟性。由於子彈形的表面法向量會沿軸向變化，使EOF的影響程度不同，進而促使改質層內部的離子分佈更為均勻；而圓錐形奈米孔，表面法向量恆定，因此未產生與子彈形相同之現象。這些現象對於奈米孔道之應用極為關鍵，例如: 模擬生物薄膜和金屬離子檢測。

In chapter 1, we propose an efficient and convenient procedure for estimating the thermodynamic equilibrium constants of the surface dissociation/association reactions of metal oxide particles through electrophoresis measurements and a general electrophoresis model, which takes account of essentially all the relevant factors. These constants are usually experimentally estimated through a tedious potentiometric acid-base titration procedure. In addition, since several assumptions need be made, the results obtained can be unreliable, especially when the difference between the equilibrium constant of the dissociation reaction and that of the association reaction is small. Another merit of the procedure proposed is that the site density of the surface dissociation/associations functional groups need not be known in advance so that it becomes much more convenient and efficient than previous procedures. The applicability of the present procedure is examined by applying it to the cases of SiO2 and TiO2 nanoparticles dispersed in an aqueous NaCl solution.
In chapter 2, we examined theoretically the electrokinetic behavior of a bullet-shaped nanopore modified by a functioning layer, focusing on its steric effect. The nanopore contains both fixed surface charge coming from the original bare surface, and space fixed charge from the modified layer. The results of numerical simulation reveal that the steric effect of the modified layer is crucial to the electrokinetic behavior of the nanopore. In particular, the softness of this layer is capable of influencing ionic profiles through electroosmotic flow (EOF). Unlike a conical nanopore where its surface normal vector is constant, that of the present bullet-shaped nanopore varies along the pore axis, thereby affecting the degree of EOF, which in turn, can make the ionic profile inside the modified layer more uniform. This is crucial to the applications of the nanopore, for example, in mimicking biological membranes and sensing metal ions.

誌謝 I
中文摘要 II
Abstract III
Contents V
List of Figures VII
List of Tables X
Chapter 1 Estimating the Thermodynamic Equilibrium Constants of Metal Oxide Particles Through a General Electrophoresis Model 1
1. Introduction 2
2. Modeling 5
3. Estimation of pKa and pKb 6
4. Results and discussion 7
4.1 SiO2 particles 7
4.2 TiO2 particles 10
4.3 Influence of pKa, pKb, and Ntotal 12
5. Conclusions 14
6. Appendix 15
7. References 19
Chapter 2 Electrokinetic Behavior of Bullet-shaped Nanopores Modified by Functional Groups: Steric Effect of Modified Layer 24
1. Introduction 25
2. Modeling 29
3. Results and discussion 33
3.1 Code verification 34
3.2 Influence of modified layer softness 36
3.3 Influence of the modified layer softness on ICR 45
4. Conclusions 50
5. References 52
Supplementary Information 59

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